In this section, we will introduce a compact spectral triple suitable for the study of the geometry of the magnetic \(C^*\) -algebra \({C}_B\) . The key element is a Dirac operator \(D_B\)  which is, in a sense that will be made more precise below, the square root of the
harmonic oscillator \(Q_B\)  defined in Section REF . We will prove
that our spectral triple provides a good example of a noncommutative manifold
of spectral dimension 2. Moreover, we will prove the continuous version of the
first Connes' formula appearing in [1]}.
